We'd probably questioned many times on the fate of our own character after he/she dies.

Where do you guys think someone like Arnbjorn will go?

He was once a member of the Circle of the Companions and died in his werewolf form which means that Hiricine could claim his soul for his Hunting Grounds. On the other hand his most recent allegiance is with the Dark Brotherhood and Sithis and so he is likely destined for the Void too.

I still doubt the two deities would bother to fight over an arrogant mutt like him though!

I think Sithis is the more powerful force, and thus would get Arnbjorn's soul.

Hiricine. It's pretty much stated that all Lycanthropes go to Hiricine, regardless of their allegiances in life. I suspect those who opt to not venerate the Lord of the Hunt end up as "prey".

since *I* think sithis is just the assassin version of shor, and shor couldn't claim a werewolf i doubt sithis could claim one of the hounds

Mephala and Hircine duke it out.